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Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 2N. Arrizabalaga, L. Le Treust, N. Raymond.

    On the MIT Bag Model in the Non-relativistic Limit, in: Communications in Mathematical Physics, 2017, vol. 354, no 2, pp. 641-669. [ DOI : 10.1007/s00220-017-2916-8 ]

    https://hal.archives-ouvertes.fr/hal-01343717
  • 3V. Banica, E. Faou, E. Miot.

    Collision of almost parallel vortex filaments, in: Communications on Pure and Applied Mathematics, 2017, vol. 70, no 2, pp. 378-405. [ DOI : 10.1002/cpa.21637 ]

    https://hal.archives-ouvertes.fr/hal-01170929
  • 4W. Bao, L. Le Treust, F. Méhats.

    Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime, in: Kinetic and Related Models , September 2017, vol. 10, no 3, pp. 553-571, https://arxiv.org/abs/1501.02177. [ DOI : 10.3934/krm.2017022 ]

    https://hal.archives-ouvertes.fr/hal-01101793
  • 5F. Casas, N. Crouseilles, E. Faou, M. Mehrenberger.

    High-order Hamiltonian splitting for Vlasov-Poisson equations, in: Numerische Mathematik, 2017, vol. 135, no 3, pp. 769-801, https://arxiv.org/abs/1510.01841. [ DOI : 10.1007/s00211-016-0816-z ]

    https://hal.inria.fr/hal-01206164
  • 6F. Castella, P. Chartier, J. Sauzeau.

    A formal series approach to the center manifold theorem, in: Foundations of Computational Mathematics, 2017, forthcoming. [ DOI : 10.1007/s10208-017-9371-y ]

    https://hal.inria.fr/hal-01279715
  • 7P. Chartier, M. Lemou, F. Méhats.

    Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics, in: Numerische Mathematik, December 2017, vol. 136, no 4, pp. 907-939. [ DOI : 10.1007/s00211-016-0864-4 ]

    https://hal.inria.fr/hal-01281950
  • 8P. Chartier, F. Méhats, M. Thalhammer, Y. Zhang.

    Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type, in: ESAIM: Mathematical Modelling and Numerical Analysis, September 2017, vol. 51, no 5, pp. 1859 - 1882. [ DOI : 10.1051/m2an/2017010 ]

    https://hal.archives-ouvertes.fr/hal-01636323
  • 9M. Chaussade-Beaudouin, M. Dauge, E. Faou, Z. Yosibash.

    Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases, in: Asymptotic Analysis, 2017, vol. 104, no 2, pp. 1-47, https://arxiv.org/abs/1602.00850. [ DOI : 10.3233/ASY-171426 ]

    https://hal.archives-ouvertes.fr/hal-01264125
  • 10N. Crouseilles, G. Dimarco, M. Lemou.

    Asymptotic preserving and time diminishing schemes for rarefied gas dynamic, in: Kinetic and Related Models , 2017, vol. 10, pp. 643-668.

    https://hal.inria.fr/hal-01392412
  • 11N. Crouseilles, S. A. Hirstoaga, X. Zhao.

    Multiscale Particle-in-Cell methods and comparisons for the long-time two-dimensional Vlasov-Poisson equation with strong magnetic field, in: Computer Physics Communications, October 2017, vol. 222, pp. 136-151.

    https://hal.archives-ouvertes.fr/hal-01496854
  • 12N. Crouseilles, S. Jin, M. Lemou.

    Nonlinear Geometric Optics method based multi-scale numerical schemes for highly-oscillatory transport equations, in: Mathematical Models and Methods in Applied Sciences, 2017, vol. 27, no 11, pp. 2031-2070. [ DOI : 10.1142/S0218202517500385 ]

    https://hal.archives-ouvertes.fr/hal-01323721
  • 13N. Crouseilles, M. Lemou, F. Méhats, X. Zhao.

    Uniformly accurate forward semi-Lagrangian methods for highly oscillatory Vlasov-Poisson equations, in: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2017, vol. 15, no 2, pp. 723-744. [ DOI : 10.1137/16M1059497 ]

    https://hal.inria.fr/hal-01286947
  • 14G. Da Prato, A. Debussche.

    An integral inequality for the invariant measure of a stochastic reaction–diffusion equation, in: Journal of Evolution Equations, 2017, vol. 17, no 1, pp. 197-214, https://arxiv.org/abs/1511.07133. [ DOI : 10.1007/s00028-016-0349-z ]

    https://hal.archives-ouvertes.fr/hal-01235038
  • 15S. Fournais, L. Le Treust, N. Raymond, J. Van Schaftingen.

    Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian, in: Journal of the Mathematical Society of Japan, 2017, vol. 69, no 4, pp. 1667-1714, https://arxiv.org/abs/1603.02810. [ DOI : 10.2969/jmsj/06941667 ]

    https://hal.archives-ouvertes.fr/hal-01285311
  • 16R. L. Frank, F. Méhats, C. Sparber.

    Averaging of nonlinear Schrödinger equations with strong magnetic confinement, in: Communications in Mathematical Sciences, 2017, vol. 15, no 7, pp. 1933-1945, https://arxiv.org/abs/1611.01574 - 12 pages. [ DOI : 10.4310/CMS.2017.v15.n7.a7 ]

    https://hal.archives-ouvertes.fr/hal-01397325
  • 17M. Lemou, A. M. Luz, F. Méhats.

    Nonlinear stability criteria for the HMF Model, in: Archive for Rational Mechanics and Analysis, 2017, vol. 224, no 2, pp. 353-380, https://arxiv.org/abs/1509.08637. [ DOI : 10.1007/s00205-017-1077-4 ]

    https://hal.archives-ouvertes.fr/hal-01207626
  • 18M. Lemou, F. Méhats, X. Zhao.

    Uniformly accurate numerical schemes for the nonlinear dirac equation in the nonrelativistic limit regime, in: Communications in Mathematical Sciences, 2017, vol. 15, no 4, pp. 1107-1128. [ DOI : 10.4310/CMS.2017.v15.n4.a9 ]

    https://hal.archives-ouvertes.fr/hal-01313976
  • 19F. Méhats, O. Pinaud.

    The quantum Liouville-BGK equation and the moment problem, in: Journal of Differential Equations, 2017, vol. 263, no 7, pp. 3737-3787, https://arxiv.org/abs/1512.01504. [ DOI : 10.1016/j.jde.2017.05.004 ]

    https://hal.archives-ouvertes.fr/hal-01255137
  • 20F. Méhats, N. Raymond.

    Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve, in: Annales Henri Poincaré, 2017, vol. 18, no 1, pp. 281-306. [ DOI : 10.1007/s00023-016-0511-8 ]

    https://hal.archives-ouvertes.fr/hal-01090045
  • 21T. Wang, X. Zhao, J. Jiang.

    Unconditional and optimal H2-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions, in: Advances in Computational Mathematics, 2017. [ DOI : 10.1007/s10444-017-9557-5 ]

    https://hal.archives-ouvertes.fr/hal-01576947
  • 22X. Zhao.

    A combination of multiscale time integrator and two-scale formulation for the nonlinear Schrödinger equation with wave operator, in: Journal of Computational and Applied Mathematics, 2017, vol. 326, pp. 320 - 336. [ DOI : 10.1016/j.cam.2017.06.006 ]

    https://hal.archives-ouvertes.fr/hal-01576629
  • 23X. Zhao.

    Uniformly accurate multiscale time integrators for second order oscillatory differential equations with large initial data, in: BIT Numerical Mathematics, 2017, vol. 57, no 3, pp. 649 - 683. [ DOI : 10.1007/s10543-017-0646-0 ]

    https://hal.archives-ouvertes.fr/hal-01591333

Scientific Books (or Scientific Book chapters)

  • 24M. Chaussade-Beaudouin, M. Dauge, E. Faou, Z. Yosibash.

    High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero, in: Operator Theory Advances and Application, Recent Trends in Operator Theory and Partial Differential Equations - The Roland Duduchava Anniversary Volume, Birkhäuser/Springer, 2017, vol. 258, pp. 89-110, https://arxiv.org/abs/1603.01459. [ DOI : 10.1007/978-3-319-47079-5_5 ]

    https://hal.archives-ouvertes.fr/hal-01278861

Other Publications

References in notes
  • 37E. Hairer.

    Geometric integration of ordinary differential equations on manifolds, in: BIT, 2001, vol. 41, pp. 996–1007.
  • 38E. Hairer, C. Lubich, G. Wanner.

    Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, Second edition, Springer Series in Computational Mathematics 31, Springer, Berlin, 2006.
  • 39E. Hairer, G. Wanner.

    Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics 14, 2, Springer-Verlag, Berlin, 1996.
  • 40C. Lubich.

    A variational splitting integrator for quantum molecular dynamics, in: Appl. Numer. Math., 2004, vol. 48, pp. 355–368.
  • 41C. Lubich.

    On variational approximations in quantum molecular dynamics, in: Mathematics of Computation, 2009.
  • 42J. M. Sanz-Serna, M. P. Calvo.

    Numerical Hamiltonian Problems, Chapman & Hall, London, 1994.


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